I use 3/16" medium orthodontic rubber bands with Cherry profile. They are perfect for Cherry profile, too thin for OEM profile.
Cherry keycaps may look like short profile, but they actually have the same travel distance as any other profile.
The travel distance without O-rings is always 4 mm with or without keycaps. When you bottom out, the slider hits the bottom of the switch housing, and there is still a gap between the top of the switch and the struts inside the keycap. The size of this gap
is different between different types of keys, but always large enough so that the keycap never touches the switch's top housing.
When you install O-rings, you put them inside that gap and only then does the size of the gap affect the travel distance. Some keycaps, like SP's DCS profile do not even have any struts so they don't work with O-rings, and you would instead have to do the "trampoline mod" with the switches themselves to get dampening.